This invention, which is a result of a contract with the U.S. Department of Energy, relates generally to methods and systems for measuring mechanical properties of materials, and more specifically to improvements in microindentation methods for measuring mechanical properties of materials.
There are numerous applications in which a dynamic measure of the stiffness and contact area between two bodies is an important factor. For example, a mechanical properties microprobe can provide a wide range of material properties from a simple microindentation test if properly instrumented. The measurements of yield strength, creep resistance, stress relaxation, modulus, fracture toughness and even fatigue are possible. Other applications in which a dynamic measure of contact area is necessary include electronic characterization of materials using point probes such as in the semiconductor industry, micromachining techniques for use in making controlled submicron scratches to produce lithographic masks, thin film properties and thickness measurement, and surface coating quality control.
The contact area between two bodies is difficult to determine when the area of contact is less than a few square microns. Prior art techniques for obtaining such measurements include measuring the physical interference (depth of contact) between the bodies and measuring the electrical resistance at the junction. In another method, the contact area between sample and indenter may be measured optically after the indenter is removed and the assumption is made that the area does not change on unloading. Each of these methods have several drawbacks that limit their usefulness.
Although imaging indents does give a direct measure of the area of contact, it becomes more difficult as the size of the indent is reduced. Submicron sized indents can only be imaged using electron microscopy. The techniques used are time consuming and only yield the final size of the indent.
One geometric characteristic of the indent that is more easily measured and can be measured continuously during the entire indentation process is the displacement of the indenter after contact. This measurement provides several other distinct advantages over direct area measurement. These include the ability to sample both elastic and plastic strains, the ability to both control and monitor stress and strain rates, and finally the elimination of the need for complicated, time consuming imaging techniques. The displacement can be measured with sufficient resolution to characterize extremely small indents; however, mathematical models of the indentation process must be employed to allow the contact area to be calculated. These models have been developed and used successfully. Further details of the models and their successful use may be found in the following references, the subject matter of which is included herein by reference thereto.
1. W. C. Oliver, R. Hutchings, and J. B. Pethica, "Measurements of Hardness at Indentation Depths as Low as 20 Nanometers"; pp 90-108 in ASTM Special Technical Publication No. 889, 1986.
2. S. I. Bulychev, V. P. Alekhin, M. K. H. Shorshorov, A. P. Ternovskii and G. D. Shnyrev, Zayod. Labor., 41(9) (1975).
An ultra low force indentation system sold under the trade name Nanoindenter is commercially available from Microsciences, Inc., Norwell, MA 02061. This system, modified according to the present invention, is shown schematically in FIG. 1. In this system, measured force is applied to the indenter electromagnetically and can be ramped up and down linearly over a range of rates. The area of the indentation is determined as a function of displacement of the indenter by measuring the displacement of the indenter after contact with the sample by means of a capacitive displacement gage. The area of the contact is a critical parameter, especially as the indented area becomes smaller and smaller, e.g., &lt;a few microns.sup.2.
Further information can be obtained from an indentation test consisting of a series of loading and unloading sequences going to progressively higher maximum loads. Thus, by loading and unloading the indenter, a plot of load versus indenter displacement is obtained which permits determination of both plastic (permanent) and elastic (resilient) deformation properties for the material being tested. Displacement measurements made during loading sequences in which the size of the indent is increased plastically, contain information about both the elastic and plastic strain fields. The unloading data represents the response of the elastic field only. Using information from both sequences of data, the plastic and elastic components can be separated; hence, the contact area, the hardness, and the modulus can be calculated, using the mathematical models for the material, for each point at which an unloading sequence begins using the relationships set forth below in equations (1) through (4).
The contact stiffness S=dP/dh.sub.T for two bodies in contact under load P, h.sub.T being the displacement of the indenter body beyond the point of contact, is measured directly at each unloading point which is the slope of the unloading curve at that point. This stiffness measurement along with the measured load, or contact force, P and the displacement h.sub.T is used to determine the various mechanical properties of a sample under test in accordance with the following relationships: EQU h.sub.I =h.sub.T -.epsilon.(P/S) (1)
where:
h.sub.I =the plastic depth of the indent, or contact area depth (see FIGS. 3 and 4); and PA1 .epsilon.=an experimentally determined constant related to the indenter geometry. PA1 P=the applied DC load. PA1 E.sub.r =Composite modulus of indenter and specimen, i.e., ##EQU1## where: E.sub.I =Modulus of Indenter; PA1 .gamma..sub.I =Poison's Ratio of Indenter; PA1 E.sub.s =Modulus of Sample; and PA1 .gamma..sub.s =Poison's Ratio of Sample.
Knowing h.sub.I, the area of contact (A) is determined as a function of h.sub.I as follows: EQU A.perspectiveto.f(h.sub.I). (2)
Once the area of contact A has been determined, the hardness (H) of the sample may be determined from the following relation ship: EQU H=P/A (3)
where:
Once the above parameters are known, the modulus of the sample may be determined from the following relationship: EQU S.perspectiveto.(2/.sqroot..pi.).sqroot.A(E.sub.r) (4)
where:
While the above sequence of measurements can yield important information on various mechanical properties of materials, repeated loading and unloading sequences cause problems with some materials due to the effects of changes in the strain rate on the properties measured, since the loading sequence must be interrupted to make the stiffness measurements. Thus, there is a need for an improved method of measuring the elastic stiffness of contact between two bodies which allows continuous measurement of stiffness. Further, there is a need for a method to not only continuously measure the stiffness of a contact between two bodies, but also continuously provide the true contact area between the two bodies.